AS Daily A Level Physics question
A student has a metal tube of fixed length that is open at both ends and resonates at its fundamental frequency of 240 Hz in air at room temperature. She covers one end to make it closed at one end, without changing the length or the air conditions. What is the new fundamental frequency of the tube?
Answer
The correct answer is B.
Correct: B — 120 Hz. A open–open tube has L = λ/2 at the fundamental, but closing one end changes the boundary condition to node–antinode so L = λ/4, halving the fundamental frequency for the same sound speed: 240 Hz → 120 Hz. A 240 Hz: wrong, this assumes boundary conditions do not affect the harmonic series. B 120 Hz: correct because the fundamental for a closed–open tube is at half the frequency of an open–open tube of the same length. C 480 Hz: wrong, doubling frequency would require halving the length, not closing an end. D 60 Hz: wrong, this is a quarter of the original frequency; closing one end halves the fundamental, not quarters it.